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Asymptotics of eigenvalues in a problem of high even order with discrete self-similar weight


Authors: A. A. Vladimirov and I. A. Sheipak
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 24 (2012), nomer 2.
Journal: St. Petersburg Math. J. 24 (2013), 263-273
MSC (2010): Primary 34L20
DOI: https://doi.org/10.1090/S1061-0022-2013-01237-4
Published electronically: January 22, 2013
MathSciNet review: 3013324
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Abstract: Spectral asymptotics for the boundary problem $ (-1)^n\,y^{(2n)}-\lambda \rho y=0$, $ y^{(k)}(0)=y^{(k)}(1)=0$, $ 0\leq k<n$, is studied in the case where the order $ 2n$ of the equation satisfies the inequality $ n>1$, and the weight $ \rho \in W_2^{-1}[0,1]$ is the generalized derivative of a self-similar function $ P\in L_2[0,1]$ of zero spectral order.


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Additional Information

A. A. Vladimirov
Affiliation: A. A. Dorodnitsyn Computing Center, ul. Vavilova, 40, Moscow 119333, Russia
Email: vladimi@mech.math.msu.su

I. A. Sheipak
Affiliation: Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Leninskie gory, Moscow 119992, Russia
Email: iasheip@mech.math.msu.su

DOI: https://doi.org/10.1090/S1061-0022-2013-01237-4
Keywords: Differential operator, self-similar function, spectral asymptotics
Received by editor(s): November 6, 2010
Published electronically: January 22, 2013
Additional Notes: The authors were supported by RFBR (grants nos. 10-01-00423, 11-01-12115-ofi-m-2011, and 09-06-00125)
Article copyright: © Copyright 2013 American Mathematical Society